Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system
This paper deals with fractal Van der Pol damped nonlinear oscillators equation having nonlinearity. By combining the techniques of the Laplace transform and the variational iteration method, we establish approximate periodic solutions for the fractal damped nonlinear systems. In this simple way, no...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2023-09-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/14613484221149515 |
| _version_ | 1827856654213840896 |
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| author | Yanni Zhang Zhen Zhao Jing Pang |
| author_facet | Yanni Zhang Zhen Zhao Jing Pang |
| author_sort | Yanni Zhang |
| collection | DOAJ |
| description | This paper deals with fractal Van der Pol damped nonlinear oscillators equation having nonlinearity. By combining the techniques of the Laplace transform and the variational iteration method, we establish approximate periodic solutions for the fractal damped nonlinear systems. In this simple way, nonlinear differential equations can be easily converted into linear differential equations. Illustrative examples including the Van der Pol damped nonlinear oscillator reveal that this method is very effective and convenient for solving fractal nonlinear differential equations. Finally, comparison of the obtained results with those of the other achieved method, also reveals that this coupling method not only suggests an easier method due to the Lagrange multiplier but also can be easily extended to other nonlinear systems. |
| first_indexed | 2024-03-12T12:27:58Z |
| format | Article |
| id | doaj.art-a56e3edd0aee42e5a2a1be4e7093361f |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-03-12T12:27:58Z |
| publishDate | 2023-09-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-a56e3edd0aee42e5a2a1be4e7093361f2023-08-29T19:09:33ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462023-09-014210.1177/14613484221149515Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol systemYanni ZhangZhen ZhaoJing PangThis paper deals with fractal Van der Pol damped nonlinear oscillators equation having nonlinearity. By combining the techniques of the Laplace transform and the variational iteration method, we establish approximate periodic solutions for the fractal damped nonlinear systems. In this simple way, nonlinear differential equations can be easily converted into linear differential equations. Illustrative examples including the Van der Pol damped nonlinear oscillator reveal that this method is very effective and convenient for solving fractal nonlinear differential equations. Finally, comparison of the obtained results with those of the other achieved method, also reveals that this coupling method not only suggests an easier method due to the Lagrange multiplier but also can be easily extended to other nonlinear systems.https://doi.org/10.1177/14613484221149515 |
| spellingShingle | Yanni Zhang Zhen Zhao Jing Pang Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system Journal of Low Frequency Noise, Vibration and Active Control |
| title | Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system |
| title_full | Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system |
| title_fullStr | Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system |
| title_full_unstemmed | Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system |
| title_short | Approximate solutions of the fractional damped nonlinear oscillator subject to Van der Pol system |
| title_sort | approximate solutions of the fractional damped nonlinear oscillator subject to van der pol system |
| url | https://doi.org/10.1177/14613484221149515 |
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